Tuesday, January 31, 2017

What kind of title is that? A detective story with a Japanese print on its front cover?

OK, it's got my attention. And then it gets worse:

"The Black–Scholes–Merton option model was the greatest innovation of 20th century finance, and remains the most widely applied theory in all of finance. Despite this success, the model is fundamentally at odds with the observed behavior of option markets: a graph of implied volatilities against strike will typically display a curve or skew, which practitioners refer to as the smile, and which the model cannot explain. Option valuation is not a solved problem, and the past forty years have witnessed an abundance of new models that try to reconcile theory with markets.

"The Volatility Smile presents a unified treatment of the Black–Scholes–Merton model and the more advanced models that have replaced it. It is also a book about the principles of financial valuation and how to apply them. Celebrated author and quant Emanuel Derman and Michael B. Miller explain not just the mathematics but the ideas behind the models."

I have only the haziest memory of understanding puts and calls once, but this sounds fascinating! A free book to review with some serious analysis.

As is the way with Amazon Vine, it arrives the very next day and I begin to appreciate the enormity of what I've done.

Authors: theoretical physicist, mathematical economist, physicist

The text, though billed as 'for traders', name-drops Hilbert spaces in the prologue

We hit Black-Scholes really hard!

When faced with a book in a paradigm I'm barely familiar with, it's Wikipedia time. Derman and Miller's first throwaway formulae for stock volatility sends me scurrying off to random walks.

I don't think those shouty traders know much about partial differential equations or their extension to stochastic processes. This book is quant territory - I'm not surprised that most senior money managers were all at sea back in 2008.

Still, I have the map of the territory now (I re-read the very clear Wikipedia article on call options) so it's time to get back to the book.

I'm looking forward to writing a semi-informed review .. at some point.

Sunday, January 29, 2017

This post in homage to wonderful AI systems such as IBM's Deep Blue, Google's DeepDream and the marvels emanating from DeepMind.

---

Alarms screamed, speakers blared, screens flared red. The nerve centre of US Western Command snapped to high alert. The indicators showed a missile launch from the Pacific, heading for San Francisco.

The new President's aggressive stance towards the Asian powers had already ratcheted tensions. New missile defense platforms had been rushed into service. Perhaps the key issue was real time sensor integration and classification.

With so much data pouring in, how could any one person figure what the hell was going on?

Skubtech inc had won the contract with its innovative deep learning platform. A highly-tuned convolutional neural network running on tens of thousands of cores, it was plugged into every radar, optical, thermal and human tactical asset of Western Command.

The OC called up his Skubtech chatbot interface.

"What the f***'s coming my way?" he demanded.

The chatbot murmured reassurance in its breathless Scarlett Johansson voice; the General began to relax, mentally preparing to stand down from DEFCON 1.

---

The missile wasn't at all accurate, it airburst five miles off the coast. It wasn't the EMP or the thermal flash which did the damage. The shock wave from the multi-kiloton fireball slammed onto the ocean surface: which triggered the San Andreas fault.

It was the big one.

---

Congressional investigators interviewed the CTO of Skubtech. He explained that the AI had been trained on hundreds of submarine missile launches.

"The North Koreans really haven't mastered submarine launches," he told the committee.

"The missile emerged from the sea and promptly set off towards North Korea. Eventually it veered around and took a circuitous path towards the American shoreline. Really, the CNN had never experienced anything like it."

The investigators had been thorough, and were not about to accept this bland reassurance as any kind of answer. They had their whistleblowers inside the company.

"This is not the first time your AI has misclassified. In internal trials, we've been led to believe that your product systematically overfits.

"Not sure that the written explanation of the final test board makes sense. If X plays next then X plays 1 and wins. If O plays next then O plays 2 and wins. So why are we told about e.g. "If O plays 3"...?"

My response: It is X to go next. The options I document reflect the structure of the game tree from this board position onwards.

"The Logic presented in Lecture 7 is strongly Classical: ¬¬P = P and ¬P v P = True. One may need to reflect on how universally applicable this is in the full AI context (e.g. Databases with incomplete information, etc)."

My response: I think that's normal for a first, undergraduate course on computational logic. There's a large and diverse literature on how to cope with more open worlds.

"So is it : "Minimax Depth 4 solves 3 X 3 noughts and crosses" but Depth 3 might not? The "Infant's Brain" Challenge, of course, is to determine how they can succeed without calculating a complete tree/solution. Although there are errors, in general settings the (advanced) Infant performance is superior... I am not sure that ANNs are really helping understand this, as you remarked after that earlier book review."

My response: Agree that no-one really knows how toddlers brains do noughts and crosses, or most other stuff. Limitations on search depth - the *depth* parameter - put the mx-player in the hands of the heuristic evaluation function. I really did not spend a lot of time with this, either designing or testing it. It just rewards lines where you have a chance to complete and penalises lines where your opponent can, and returns the difference. One could do a lot better.The end point would presumably be an evaluation function equivalent to the competent toddler.

These Imperial College lectures date back to 2006 and 2009 (Simon Colton), but the underlying principles haven't changed. The earlier lectures (starting here) provide an introduction to AI and logic: we get to implementation at lecture 7 and subsequent.

I've chosen them for their clarity and completeness. The level of detail is that of a good overview.

We have shown how knowledge can be represented in first-order logic, and how rule-based expert systems expressed in logic can be constructed and used. We now look at how to take some known facts about a domain and deduce new facts from them. This will, in turn, enable agents to prove things, i.e., to start with a set of statements we believe to be true (axioms) and deduce whether another statement (theorem) is true or not.

We will first look at how to tell whether a sentence in propositional logic is true or false. This will suggest some equivalences between propositional sentences, which allow us to rewrite sentences to other sentences which mean the same thing, regardless of the truth or meaning of the individual propositions they contains. These are reversible inferences, in that deduction can be applied either way.

We then look at propositional and first-order inference rules in general, which enable us deduce new sentences if we know that certain things are true, and which may not be reversible.

A minor miracle occurred in 1965 when Alan Robinson published his resolution method. This method uses a generalised version of the resolution rule of inference we saw in the previous lecture. It has been mathematically proven to be refutation-complete over first order logic. This means that if you write any set of sentences in first order logic which are unsatisfiable (i.e., taken together they are false, in that they have no models), then the resolution method will eventually derive the False symbol, indicating that the sentences somehow contradict each other.

In particular, if the set of first order sentences comprises a set of axioms and the negation of a theorem you want to prove, the resolution method can be used in a proof-by-contradiction approach. This means that, if your first order theorem is true then proof by contradiction using the resolution method is guaranteed to find the proof to a theorem eventually.

To recap, we have looked at logic and some rules of deduction in order to understand automated reasoning in the general case. In the last lecture we looked at a particular rule of inference, the resolution rule. We know that the application of this rule produces a complete search method, which means that it will prove any true theorem which can be written in first order logic. Application of the rule relies on having two sentences in conjunctive normal form (CNF) where one literal of one unifies with the negation of a literal in the other. We described how to write first order sentences in CNF, and how to find unifying substitutions in lecture 8. In this lecture, we look at exactly how to use the resolution rule to prove first order theorems in practice.

We have looked at the automation of intelligent tasks using deduction to infer new information from old. We now look at the use of inductive reasoning to infer new information from old. ...

As with many areas in AI, machine learning has become fairly specialised. In this case, learning from examples dominates the field, partially because of the applications it affords. If a learning agent can look at the examples of share prices and learn a reason why some shares fall during the first financial quarter, this is of great commercial advantage. If another agent can learn reasons why certain chemicals are toxic and others are not, this is of great scientific value. If another agent yet can learn what a tank looks like given just photographs of tanks, this is of great military advantage.

As discussed in the last lecture, the representation scheme we choose to represent our learned solutions and the way in which we learn those solutions are the most important aspects of a learning method. We look in this lecture at decision trees - a simple but powerful representation scheme, and we look at the ID3 method for decision tree learning.

Decision trees, while powerful, are a simple representation scheme. While graphical on the surface, they can be seen as disjunctions of conjunctions, and hence are a logical representation, and we call such schemes symbolic representations. In this lecture, we look at a non-symbolic representation scheme known as Artificial Neural Networks. This term is often shortened to Neural Networks, but this annoys neuro-biologists who deal with real neural networks (inside our human heads).

As the name suggests, ANNs have a biological motivation, and we briefly look at that first. Following this, we look in detail at how information is represented in ANNs, then we look at the simplest type of network, two layer networks. We look at perceptrons and linear units, and discuss the limitations that such simple networks have. In the next lecture, we discuss multi-layer networks and the back-propagation algorithm for learning such networks.

We can now look at more sophisticated ANNs, which are known as multi-layer artificial neural networks because they have hidden layers. These will naturally be used to undertake more complicated tasks than perceptrons.

We first look at the network structure for multi-layer ANNs, and then in detail at the way in which the weights in such structures can be determined to solve machine learning problems. There are many considerations involved with learning such ANNs, and we consider some of them here. First and foremost, the algorithm can get stuck in local minima, and there are some ways to try to get around this.

As with any learning technique, we will also consider the problem of overfitting, and discuss which types of problems an ANN approach is suitable for.

I'm hyper-wary of the fluffy-bunny pleasantries of the Standard Social Science Model, but it seems well-regarded so I'm taking the risk. Should be out some time in late February.

---

Do you hear that hacking cough from the bedroom? Clare is much recovered today but the sub-zero windchill of our lunchtime shopping trip to Waitrose has sapped her energy .. and she has retired to bed. Still, direction of progress is positive.

(defvar *win-score* 32) ; the score assigned to a terminal win position
(defvar *lose-score* -32) ; the score assigned to a terminal lose position
(defvar *draw-score* 0) ; the score assigned to a terminal draw position

;; -------------------- GAME FRAMEWORK -----------------------------------
;;
;; The game is about boards, not nodes or trees. Those are purely internal
;; to tree-search players.
;;
;; The function 'play' takes functional arguments as players
;;

Tuesday, January 24, 2017

Clare has retired to bed with a heavy cold, shivering under a duvet, a second duvet and a fleece, despite both radiators being on. I tell her she looks like something out of a mediaeval plague scene, perhaps Hieronymus Bosch?

She opens a bleary eye and croaks.

My complementary immune system is functioning just fine. Did weights yesterday - pretty much the whole programme - and today spun the exercise bike for 18 minutes and 14 seconds to burn 200 Calories. That was breakfast.

I have spent most of the day debugging my noughts and crosses program. First the function that builds the game tree didn't work: I had mentally elided the distinction between the tree-building function recursively 'switching sides' as it constructs alternating plies of crosses and noughts down the tree .. vs. the need to continually remember which side the player is actually playing so you can distinguish a win from a loss. You need two parameters, not one.

Silly that.

Now the minimax function, which traverses that tree and bubbles terminal scores to the top (alternating between propagating minimum and maximum subtree values) is playing up - but only some of the time.

Both these functions are deeply recursive and quite general to any tree-search program. At this point the bugs are subtle .. and I have given up for the day.

I hope to dump the working code here one of these days. It's harder (when you do generalised tree-search) than one might initially think.

Monday, January 23, 2017

The presenter is beautifully turned out. She started her career on a well-regarded archaeology show but has blossomed into every public broadcaster's dream of a popular science presenter. She's attractive, well-informed and of impeccable views.

As befits a photogenic media star, she is also a professor at one of our better universities.

The archaeologist she is interviewing is old-school. His teeth aren't right, his clothes an afterthought and his accent atrocious.

"This hill fort," she says pointing to it, "There's the ditch and wall surrounding it, and this curious set of angled avenues making the entrance diagonal, with sharp turns before you can ..."

"It's consistent with a band of attackers being repulsed with heavy casualties and their ..."

"On the other hand, many scientists think what we're seeing here are the results of a sky burial, where the bodies of the revered dead were offered to wildlife and then the bones carefully decorated and buried. There's been a great deal of time for ground-disturbance of course."

His face set, the archaeologist turns his attention to the table, where bronze swords have been laid out. But he's too slow.

"These swords, quite corroded now, show the beautiful craftsmanship of grave goods or perhaps marks of status for the most elite leaders. You can see how much effort has gone into them as prestigious works of art ..."

At this point, the set is invaded by a young man draped in a black flag and toting a Kalashnikov. He shouts religious slogans and brings his weapon to bear.

It's been a recurring theme here that advanced capitalism - in its current form - selects against its own continuing existence.

The reason is very simple: it needs smart people to operate it, yet it rewards such people with careers so intensive and perhaps so interesting that they don't reproduce much. They are outcompeted by people who do not share their gifts for conscientiousness, affability and general competence.

I think it was La Griffe du Lion who first wrote about smart fraction theory, observing that modern societies are complex networks of interdependencies which need a level of cognitive competence to make them work at all.

Basically, when you don't have enough smart, conscientious people the bureaucracies don't function, stuff doesn't get maintained, institutions break down or can't be created in the first place.

Garett Jones updated and popularised this argument in his book, Hive Mind. I reviewed it here.

---

La Griffe empirically set the smart fraction edge at (verbal) IQ = 106, but I'm going to be more conservative (perhaps AI will help?) and set it at 105. Let's look at four areas of the world, with differing average IQs and see what fraction of the population constitutes the smart fraction.

First China and Japan, with an average IQ of 105. Half the population counts as their smart fraction. We know what those societies can do.

(La Griffe would use ~100 for the North-East Asian verbal IQ here - his correlations show best fit of verbal IQ with capitalist success. Other races don't show a divergence between verbal IQ and general IQ, see La Griffe's article for more. I tend to think that all those engineers with their enhanced visuospatial abilities are doing wonders with the GNP.)

Secondly, Western Europeans ('Caucasians') with average IQ 100. The smart fraction is the 37% of the population with IQ ≥ 105. These societies seem more dysfunctional than East Asia but still work most of the time.

Thirdly, the Middle-East with an average IQ of 85. Here we have countries like Egypt and Iraq, where only 9% of the population have an IQ ≥ 105. These are societies which don't function in a healthy way - corruption is endemic and innovation is poor to non-existent.

Finally we come to Africa, where the most optimistic estimated average IQ is 75. Here only about 2.3% of the population constitute the smart fraction. Given this tiny percentage, it's no surprise that advanced capitalist societies simply don't exist, or those previously built in region cannot be maintained.

---

The US Government Department of Labor Bureau of Labour Statistics publishes a detailed spreadsheet showing employed persons by detailed occupation, sex, race, and Hispanic or Latino ethnicity across 149 million people.

Ethnic/gender correlations with IQ/personality-type prerequisites of jobs are striking.

It was the development of large-scale societies in the neolithic revolution which kicked off selection for the kinds of cognitive skills which are only required in complex societies.

It's taken ten thousand years to drive human intelligence up a couple of standard deviations (30 IQ points).

According to the latest, detailed study from Iceland, the fertility-reduction of our smart fraction is decreasing average IQ by 3 points per century: 15 points in 500 years if the trend continues.

At this rate, a mere one thousand years would be enough to wind us back to hunter-gather levels.

---

With fewer competent people being born, skill-shortages increase for the more complex roles. Standards are lowered while performance drops .. and drops.

Unless the right-hand side of the cognitive bell curve starts having large families as the norm, in a few centuries our western societies are going to look a lot like Egypt or Iraq today. After that it will get worse.

Saturday, January 21, 2017

"When someone talks about AI, or machine learning, or deep convolutional networks, what they’re really talking about - as is the case for so many computing concepts - is a lot of carefully manicured math.

At the heart of these versatile and powerful networks is a volume of calculation only achievable by the equivalent of supercomputers. More than anything else, this computational cost is what is holding back applying AI in devices of comparatively little brain: phones, embedded sensors, cameras. ...

Machine learning, Farhadi continued, tends to rely on convolutional neural networks (CNN); these involve repeatedly performing simple but extremely numerous operations on good-sized matrices of numbers. But because of the nature of the operations, many have to be performed serially rather than in parallel. ...

It’s the unfortunate reality of both training and running the machine learning systems performing all these interesting feats of AI that they feature phenomenally computationally expensive processes.

“It’s hard to scale when you need that much processing power,” Farhadi said. Even if you could fit the “beefy” - his preferred epithet for the GPU-packed servers and workstations to which machine learning models are restricted - specs into a phone, it would suck the battery dry in a minute.

Meanwhile, the accepted workaround is almost comically clumsy when you think about it: You take a load of data you want to analyze, send it over the internet to a data center where the AI actually lives and computers perhaps a thousand miles away work at top speed to calculate the result, hopefully getting back to you within a second or two."

"It’s not such a problem if you don’t need that result right away, but imagine if you had to do that in order to play a game on the highest graphical settings; you want to get those video frames up ASAP, and it’s impractical (not to mention inelegant) to send them off to be resolved remotely.

But improvements to both software and hardware have made it unnecessary, and our ray-traced shadows and normal maps are applied without resorting to distant data centers.

Farhadi and his team wanted to make this possible for more sophisticated AI models. But how could they cut the time required to do billions of serial operations?

“We decided to binarize the hell out of it,” he said. By simplifying the mathematical operations to rough equivalents in binary operations, they could increase the speed and efficiency with which AI models can be run by several orders of magnitude.

Here’s why. Even the simplest arithmetic problem involves a great deal of fundamental context, because transistors don’t natively understand numbers — only on and off states. Six minus four is certainly two, but in order to arrive at that, you must define six, four, two and all the numbers in between, what minus means, how to check the work to make sure it’s correct, and so on. It requires quite a bit of logic, literally, to be able to arrive at this simple result.

But chips do have some built-in capabilities, notably a set of simple operations known as logic gates. One gate might take an input, 1 (at this scale, it’s not actually a number but a voltage), and output a 0, or vice versa. That would be a simple NOT gate, also known as an inverter. Or of two inputs, if either is a 1, it outputs a 1 — but if neither or both is a 1, it outputs a 0. That’s an XOR gate.

These simple operations are carried out at the transistor level and as such are very fast. In fact, they’re pretty much the fastest calculations a computer can do, and it happens that huge arrays of numbers can be subjected to this kind of logic at once, even on ordinary processors.

The problem is, it’s not easy to frame complex math in terms that can be resolved by logic gates alone. And it’s harder still to create an algorithm that converts mathematical operations to binary ones. But that’s exactly what the AI2 engineers did."

And they have something which works, at least in prototype.

"Farhadi showed me the fruits of their labor by opening an app on his phone and pointing it out the window. The view of the Fremont cut outside was instantly overlaid with boxes dancing over various objects: boat, car, phone, their labels read.

In a way it was underwhelming: after all, this kind of thing is what we see all the time in blog posts touting the latest in computer vision.

But those results are achieved with the benefit of supercomputers and parallelized GPUs; who knows how long it takes a state of the art algorithm to look at an image and say, “there are six boats, two cars, a phone and a bush,” as well as label their boundaries.

After all, it not only has to go over the whole scene pixel by pixel, but identify discrete objects within it and their edges, compare those to known shapes, and so on; even rudimentary object recognition is a surprisingly complex task for computer vision systems.

This prototype app, running on an everyday smartphone, was doing it 10 times a second."

I still remember programming in IBM System/360 Assembler. I later discovered that every assembly language I had ever used was itself further compiled to/interpreted by microcode.

Friday, January 20, 2017

"Women on average have a strong preference for working with people - hence the nurses and teachers; and, compared to men, they care more about family and relationships and have broader interests and priorities—hence little appeal in becoming CEOs. Men have far more interest in "things" - hence the engineers ... "

I'm sitting here looking at a short recursive function which returns a tree whose nodes are themselves a complicated data-type (Atom-list x Nat x Nat) and I'm trying to do minimax on it. The Lispworks 'Listener' has replaced the Atom lists with hash signs (why?) and the arithmetic min function complains it's getting something weird rather than Real - and has thrown me into the debugger.

Why?

The code looks good, although there are so many good-practice projector and constructor functions, cluttering the text.

I sit in frustration, trying to visualise the unwrapping of the computation as the nested mutually-recursive functions execute their combined paths to disaster. Part of me wants to chuck this code away; another part muses that this would mean I was getting even more stupid in my old age.

I review the psychological characteristics required for successful programming.

Obsessional perseverance when nothing goes right and time-wasting options beckon.

If ever an occupation required what Simon Baron-Cohen calls the 'systemizing brain', this is it.

---

Update: (Twenty minutes later).

OK, so it was a type clash. I forgot to update a previous sub-function. Needed to add some projectors. So now I have a result.

Shame it's not the one I actually need ...

---

Some print-journalism stays with you. I regularly recall a right-on female commentator on The Times using her column to weigh in on gender equality in programming. After some shocking statistics she recounts how she asked her daughter if she had considered becoming a programmer. Her daughter looks at her as if she is mad: "Why would I want to do anything as boring as that?"

The daughter's mother is not of course a programmer. She's an opinion-piece journalist, a job where you get to meet and socialise with important people and then write lots of stuff of interest to your like-minded pals.

*Sigh*.

---

In case it isn't obvious, I know there are good female programmers. I know there are good female physicists (see here). It's just .. we're talking distributions here - you know, bell-shaped curves? - and the male-female means are noticeably different.

Strive for equality of opportunity; do not expect equality of outcome.

Thursday, January 19, 2017

So this evening was the second time in two months that I've experienced a scotoma.

"5th November 2016. After weights exercise, a visual illusion to the right of central visual field (both eyes separately). A flickering jagged arc. This is consistent with a scotoma. Same phenomenon with either eye closed. After half an hour it began to move out and enlarge while retreating further into peripheral vision. After an hour it disappeared.

This phenomenon reappeared 19th January 2017, a couple of hours after fairly intense exercise, at 6.10 pm. Visible duration 20 minutes. Started at the centre of the visual field, a flashing-lightning V-shape with vertex at 8 o'clock. Gradually got larger until it vanished past the boundary of the visual field.

Other relevant information: I skipped lunch today as part of my weight-control programme."

"f you read the title and opened this post, you most likely do suffer from Scintillating Scotoma. You know, start to lose part of vision because of a flashing spot .. . The flashing zig-zag moves to outer edge of eyes, then, after 20 minute or so, goes away.

The common consensus is that is a migraine headache, without the pain.

Anyhow, since I started upping my intensity on the bike trainer workouts, I seem to be getting them after each workout. Could it be clustering since the intensity is greater? I used to get them sometimes after early season races, then as the season wore on and I got used to the intensity, they went away.

I know they're not really an issue, but, hard not go to into a mini-panic each time. "

"a wave of electrophysiological hyperactivity followed by a wave of inhibition. Spreading depolarization (SD) describes a phenomenon characterized by the appearance of depolarization waves of the neurons and neuroglia that propagates across the gray matter at a velocity of 2–5 mm/min.

SD can be induced by hypoxic conditions and facilitates neuronal death in energy-compromised tissue. SD has also been implicated in migraine aura, where SD is assumed to ascend in well-nourished tissue and is typically benign in most of the cases, although it may increase the probability in migraine patients to develop a stroke."

I don't suffer from migraine, and the effect is purely visual although if pressed, I might admit to an ill-defined feeling of 'headiness' which persists for rather longer.

"Brian Greene in ‘The Fabric of the Cosmos’ (page 134) considers an alien in a galaxy ten billion light years away, at the edge of the visible universe. Simply by ambulating towards or away from us at 10 mph, the alien’s view of what is happening ‘right now’ on earth swings from 149 years in the past to 149 years in the future."

Still, the block universe is classical and therefore inaccurate. It's necessary to move to quantum theory where, as usual, one needs to take the red pill.

"In FAPP (For All Practical Purposes) language we have a quantum mechanical system described by a wave function ψ(t), I am only interested in the time variable.

The wave function obeys a Schrödinger equation with a Hamiltonian H. The formal solution to this equation is ψ(t) = exp(iHt)ψ(0). Throughout I am setting ћ = 1. Thus to recover Ψ(0) from ψ(t) all we have to do is to multiply by exp(-iHt).

Haven’t we then recovered the past? What is all the fuss about? The problem is that there is more to life than the wave function. There are the “observables” which represent what we really want to know about the system. These observables are described by Hermitian operators A. B. C and so on. We can expand ψ in a sum over the orthonormal eigenfunctions of any of these operators. The coefficients in the expansion are related to the probabilities that in a measurement the system will be found to have one of these eigenvalues. This is “Born’s rule” and in FAPP it must be assumed.

To find which of these eigenvalues the system actually has, we must perform a measurement. Stripped to its essence the apparatus that produces this measurement projects out from the sum of eigenfunctions one of them.

After the measurement the rest of the terms in the sum disappear. Using the term of art, the wave function “collapses”. It is at this point that we lose our capacity to reconstruct the past.

Projection operators are singular. They do not have inverses. All the king’s horses and all the king’s men cannot put the wave function back together again.

It was von Neumann in the early 1930’s who first noted that in FAPP mechanics there were two kinds of processes. There were processes that could be described by a Schrödinger equation and there were measurements which could not. He did not, as far as I know, comment on what this implied for retrodiction.

A case in point is an electron described by a spherically symmetric Schrödinger wave. If this electron strikes a detector is does so at a place - a spot. After this happens all trace of the spherically symmetric wave function vanishes.

I have certainly not made a careful search of the literature but among the founding fathers of FAPP I can come up with only two references that deal with the matter of the quantum past.

One is Heisenberg and the other is a paper by Einstein, Richard Tolman, and Boris Podolsky, “Knowledge of Past and Future in Quantum Mechanics” which they wrote in 1931 when Einstein was spending time at CalTech."

Bernstein talks about these two references, and then discusses where he thinks the problem resides, and what is to be done.

"It seems to me that any interpretation of the quantum theory that addresses this [the problem of wavefunction collapse] must have the feature that measurements are simply just another interaction like the rest.

Von Neumann’s notion that there were two classes of interactions one whose time evolution could be described by a Schrödinger equation and one of which couldn’t, has to be abandoned.

I will discuss two proposals for doing this each of which has its adherents and its detractors. On the one hand I am going to discuss what I will call “Bohmian mechanics” a term which David Bohm, who invented this approach , apparently did not like. As far as he was concerned, he was just doing quantum mechanics but in a different way. However nearly everyone else calls it Bohmian mechanics - so will I.

On the other hand, I am going to discuss the “decoherent history” interpretation which Murray Gell-Mann and Jim Hartle have done the most on. Sometimes this is called the “many worlds” interpretation, but not by them. I think that the term “many worlds” is misleading. As far as we know there is one world, the one we live in."

I'm not a fan of “Bohmian mechanics” and insofar as any quantum ontology works for me, it has to be "Many Worlds" (Sean Carroll explains why).

So I'll skip over Bernstein's description of Bohm's view of the quantum past and quote his take on “decoherent histories”.

"In the "Many Histories Interpretation" what indeed is history?

At first sight this might seem to be obvious. All we have to do is to run the chain backwards.

Yes this gives one history but there are others, possibly very many others. The reason is that if all we know is the present state vector there are many paths by which we could have arrived there depending on which initial state vector we started from. We have no way of knowing this from the data we have at hand.

Let us take an example discussed by Hartle - the Schrödinger cat (I can’t resist noting that when I spent an afternoon with Schrödinger in his apartment in Vienna there was no cat). In any event this unfortunate feline is put in a box that contains a capsule of poison gas and a sample of uranium. The capsule is triggered so that if the uranium has an alpha decay, the alpha sets off the trigger and the unfortunate feline expires.

After a time interval we open the box and happily the cat is alive. It could, according to the many history approach have arrived at this state in two ways. The initial state might have been a cat alive state or it might have been a coherent sum of a cat alive and a cat dead state. From the presence of the living cat we cannot decide.

The vision of the past given by the decoherent history interpretation and the Bohmian seems radically different. In Bohmian mechanics we could in principle follow all the cat molecules backwards in time and arrive at one and only one past.

I don’t know how you feel, but the ambiguity of the past makes me queasy. It might be entertaining to imagine that in an alternate past my grandmother who was born in a Polish stetl could have been Eleanor Roosevelt.

I readily accept that these pasts to not communicate but there seem to be too many of them from the point of view of economy. A trip to a barber wielding Occam’s razor seems warranted.

In any case when it comes to quantum pasts, as Duke Ellington taught us, “Things ain’t what they used to be.”

Perhaps Bernstein wrote this short paper just for that final joke at the end?

To summarise, if you take quantum theory seriously and you take eternalism (the block universe) seriously, then it seems that the past is as indeterminate as the future.

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How does this relate to the 'low entropy in the past' idea used to explain the 'arrow of time'?

Since quantum theory is consistent with the second law of thermodynamics, a picture emerges of backwards branching towards (superpositions of) Big Bang variants.

Wednesday, January 18, 2017

"Many people resist the implication that this theory is good enough to account for the physics underlying phenomena such as life, or consciousness. They could, in principle, be right, of course; but the only way that could happen is if our understanding of quantum field theory is completely wrong.

When deciding between “life and the brain are complicated and I don’t understand them yet, but if we work harder I think we can do it” and “I understand consciousness well enough to conclude that it can’t possibly be explained within known physics,” it’s an easy choice for me."

Carroll summarises our complete theory of the universe in one equation. As he points out, "No experiment ever done here on Earth has contradicted this model."

For the physicist, life is merely a parameter subspace in the evolution of the universal wavefunction. I'm tempted to mention cats. The physicist is professionally a psychopath. So note that the next time a famous physicist expresses an opinion on politics or public policy. They are talking outside their discipline.

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It's not wrong to start with physics, how could it be? But we seek more enlightenment from biology. At least the subjects we study there are actually living.

The title of this post is the meaning of life. Did you see the word 'human' anywhere?

Consider the plants and animals, the germs and fungi, occupants of this planet for four billion years. Darwin gave us the answer - the meaning of life is to survive and have reproducing progeny. All those ancestral entities which didn't 'get that' were eliminated from reality.

And for most creatures, there is no more meaning than that. If they were to waste their time and energy on doing anything else, they would be outcompeted and removed from the gene pool.

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On to sociology. It seems unbearable to a cultured person in the twenty first century that the meaning of their life is reduced to the number of child-bearing children they manage to create. This has thrown reductionist biologists into confusion.

I once read that the reason Catholic priests were celibate was some variation of the alleged 'gay uncle' phenomenon. Utterly delusional.

To state the obvious, humans are social creatures and large-scale agrarian societies rapidly outcompeted hunter-gathers. Almost all contemporary humans are the descendants of individuals who successfully adapted to living in large-scale cooperative societies.

Until the recent advent of contraception, reproductive success was strongly linked to social status. Social status in large-scale societies selects for social accomplishment: it helps to be good at something people value, and not to be a muppet.

A desire simply to breed is not really enough: your neighbours can get lethally irritated.

It's surprising how many people delude themselves that being an actor, a rock star, a politician or a top executive or even intellectual is not about getting the girl (or, if a girl, getting a better class of admirer).

What do you think?

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Social creatures have complex life histories, no longer purely individualistic. We all recall "Haldane famously joking that he would willingly die for two brothers or eight cousins."

Those celibate Catholic priests are using prosocial psychological drives to inhibit their more primal reproductive imperatives. No society could cohere without such inhibitory mechanisms and since the ages of rape and pillage of outgroups, there has been selection for male self-control.

As ever, there is variation in the population and a celibate occupation strongly selects within that.

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Some conclusions. The biologists are right: for humans the meaning of life is in some extended sense to have offspring. A society which fails to reproduce abolishes itself and vanishes from reality. The extended sense means that we could profitably devote our lives to aiding close kin, or even those whose social-solidarity benefits our kin (the foundation of reciprocal altruism).

We all benefit from the continuing integrity of our societies with their high carrying capacities.

It's OK to be a celibate, rule-abiding priest .. really. Even if you are professionally confused about the meaning of life.